Mathcad Professional 14.0 <description/> <author/> <company/> <keywords/> <revisedBy>IaDot</revisedBy> </userData> <identityInfo> <revision>13</revision> <documentID>2B788B01-96FD-4AF3-AE5F-9B6E5F926E51</documentID> <versionID>AD1EBFF3-95C6-4CB9-911C-115EBC8C7DFB</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="#00f"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr 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tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000080"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <decimal precision="1" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="true" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="true" page-width="612" page-height="792"> <margins left="54" right="36" top="36" bottom="41.76"/> <header use-full-page-width="false"/> <footer use-full-page-width="true"> <left>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss\fprq15 Arial;}} \viewkind4\uc1\pard\f0\fs18 Project Name\f1\par }</left> <center>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15\fcharset0 Arial;}{\f1\fswiss Arial;}} \viewkind4\uc1\pard\qc\f0\fs18 Plastic Moment - Negative Section\f1\fs20\par }</center> <right>{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fswiss\fprq15 Arial;}{\f1\fswiss\fprq15\fcharset0 Arial;}} \viewkind4\uc1\pard\qr\f0\fs18\{d\}\f1 \{n\} of \{nn\}\f0\par }</right> </footer> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="us" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="true" ruler-unit="in"> <tabs> <tab show-guide="false" position="4.5"/> <tab show-guide="false" position="27"/> <tab show-guide="false" position="45"/> <tab show-guide="false" position="63"/> <tab show-guide="false" position="81"/> <tab show-guide="false" position="99"/> <tab show-guide="false" position="117"/> <tab show-guide="false" position="126"/> <tab show-guide="false" position="162"/> <tab show-guide="false" position="198"/> <tab show-guide="false" position="306"/> <tab show-guide="false" position="333"/> <tab show-guide="false" position="351"/> <tab show-guide="false" position="378"/> <tab show-guide="false" position="414"/> <tab show-guide="false" position="432"/> </tabs> </ruler> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="16250" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="16065" left="18" top="6" width="155.25" height="30" align-x="18" align-y="6" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="1" display-width="153.75" display-height="28.5"/> </picture> <rendering item-idref="2"/> </region> <region region-id="16066" left="198" top="3.75" width="307.5" height="36" align-x="213" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="16"> <b>Plastic Moment Calculation For Negative Sections </b> </f> </p> </text> </region> <region region-id="16249" left="546" top="14.25" width="382.5" height="180" align-x="546" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#800000">DOT refers to the Iowa Department of Transportation</c> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#800000">OBS refers to the Iowa DOT Office of Bridges and Structures</c> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#800000">Disclaimer: This software is intended for use by Iowa DOT personnel and consultants working for the OBS in their development of projects for the Iowa DOT. Any other use is at the sole discretion of the user. The Iowa DOT makes the software available "AS IS" and assumes no liability nor makes any warranty of any kind, including warranties of noninfringement, fitness or merchantability whether expressed or implied, to the accuracy or functionality of this software. By downloading or using this file, you are agreeing to this disclaimer.</c> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#800000">The OBS will only support those persons using this software in connection with Iowa DOT related business.</c> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#800000">Please report any errors to the Iowa DOT OBS.</c> </p> </text> </region> <region region-id="16067" left="12" top="48" width="492.75" height="20.25" align-x="12" align-y="48" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{7EFFBE60-44F5-11CE-83C5-08003601A74E}" type="static" item-idref="3"/> <rendering item-idref="4"/> </region> <region region-id="16185" left="6" top="68.25" width="516" height="15" align-x="6" align-y="78" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This worksheet calculates the plastic moment (M<sub>p</sub>) and depth to the plastic neutral (Y) axis for negative sections.</p> </text> </region> <region region-id="16186" left="6" top="92.25" width="249.75" height="36" align-x="6" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="85.5"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false">SPECIFICATION:<tab/> </inlineAttr> </b> </f>LRFD 5th Edition, 2010 (U.S. Units).<sp count="2"/> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="85.5"> <tab/>Appendix D6</p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="85.5"> <tab/> </p> </text> </region> <region region-id="16058" left="1050" top="92.25" width="103.5" height="12" align-x="1050" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Special Unit Definitions:</p> </text> </region> <region region-id="16059" left="1062" top="117" width="60" height="12.75" align-x="1080.75" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">kip</ml:id> <ml:apply> <ml:mult/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">lbf</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="16060" left="1146" top="110.25" width="42.75" height="27.75" align-x="1165.5" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">plf</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:id xml:space="preserve">ft</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="16187" left="6" top="140.25" width="481.5" height="12" align-x="6" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false">ASSUMPTIONS: </inlineAttr> </b> </f> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false">Concrete in tension shall be neglected.</inlineAttr> </f> </p> </text> </region> <region region-id="16061" left="1146" top="140.25" width="45" height="33.75" align-x="1167.75" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">psf</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ft</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="16062" left="1062" top="146.25" width="41.25" height="33.75" align-x="1080" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ksi</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kip</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="16063" left="1062" top="176.25" width="45" height="33.75" align-x="1083.75" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">pcf</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ft</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="16189" left="6" top="186.75" width="93.75" height="14.25" align-x="19.5" align-y="198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <u> <inlineAttr line-through="false"> <c val="#00f">INPUT SECTION</c> </inlineAttr> </u> </b> </f> </p> </text> </region> <region region-id="16190" left="30" top="212.25" width="72.75" height="12" align-x="39" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Deck Thickness:</p> </text> </region> <region region-id="16191" left="342" top="213" width="37.5" height="16.5" align-x="356.25" align-y="222" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="s">t</ml:id> <ml:apply> <ml:mult/> <ml:real>8</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="16192" left="30" top="236.25" width="140.25" height="12" align-x="39" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Concrete Compressive Strength:</p> </text> </region> <region region-id="16193" left="342" top="237" width="48.75" height="16.5" align-x="357" align-y="246" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:apply> <ml:mult/> <ml:real>3.5</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="16194" left="30" top="260.25" width="147.75" height="12" align-x="30" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Width of the Compression Flange:</p> </text> </region> <region region-id="16195" left="342" top="261" width="45" height="16.5" align-x="359.25" align-y="270" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">b</ml:id> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="16196" left="30" top="284.25" width="166.5" height="12" align-x="30" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Thickness of the Compression Flange:</p> </text> </region> <region region-id="16197" left="342" top="285" width="37.5" height="16.5" align-x="356.25" align-y="294" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">t</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="16198" left="30" top="308.25" width="123.75" height="12" align-x="30" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Width of the Tension Flange:</p> </text> </region> <region region-id="16199" left="342" top="309" width="43.5" height="16.5" align-x="357.75" align-y="318" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t">b</ml:id> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="16200" left="30" top="332.25" width="142.5" height="12" align-x="30" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Thickness of the Tension Flange:</p> </text> </region> <region region-id="16201" left="342" top="333" width="36" height="16.5" align-x="354.75" align-y="342" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t">t</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="16202" left="30" top="356.25" width="51.75" height="12" align-x="30" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Web Depth:</p> </text> </region> <region region-id="16203" left="342" top="357" width="41.25" height="12.75" align-x="355.5" align-y="366" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:real>64</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="16204" left="30" top="380.25" width="70.5" height="12" align-x="30" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Web Thickness:</p> </text> </region> <region region-id="16205" left="342" top="381" width="55.5" height="16.5" align-x="358.5" align-y="390" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w">t</ml:id> <ml:apply> <ml:mult/> <ml:real>.4375</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="16206" left="30" top="404.25" width="156.75" height="12" align-x="55.5" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Compression Flange Yield Strength:</p> </text> </region> <region region-id="16207" left="342" top="405" width="53.25" height="16.5" align-x="363.75" align-y="414" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yc">F</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="16208" left="30" top="428.25" width="132.75" height="12" align-x="55.5" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Tension Flange Yield Strength:</p> </text> </region> <region region-id="16209" left="342" top="429" width="51.75" height="16.5" align-x="362.25" align-y="438" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yt">F</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="16210" left="30" top="452.25" width="87.75" height="12" align-x="55.5" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Web Yield Strength:</p> </text> </region> <region region-id="16211" left="342" top="453" width="55.5" height="16.5" align-x="366" align-y="462" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yw">F</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="16212" left="30" top="476.25" width="80.25" height="12" align-x="39" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Area of Rebar Top:</p> </text> </region> <region region-id="16213" left="342" top="471" width="48" height="22.5" align-x="362.25" align-y="486" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rt">A</ml:id> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="16214" left="30" top="500.25" width="96.75" height="12" align-x="39" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Area of Rebar Bottom:</p> </text> </region> <region region-id="16215" left="342" top="495" width="50.25" height="22.5" align-x="364.5" align-y="510" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rb">A</ml:id> <ml:apply> <ml:mult/> <ml:real>0</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="16216" left="30" top="524.25" width="93" height="12" align-x="55.5" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Rebar Yield Strength:</p> </text> </region> <region region-id="16217" left="342" top="525" width="52.5" height="16.5" align-x="363" align-y="534" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="yr">F</ml:id> <ml:apply> <ml:mult/> <ml:real>60</ml:real> <ml:id xml:space="preserve">ksi</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="16218" left="30" top="548.25" width="177" height="12" align-x="55.5" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Haunch (Bottom of Deck To Top of Web):</p> </text> </region> <region region-id="16219" left="342" top="549" width="69" height="12.75" align-x="381" align-y="558" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Haunch</ml:id> <ml:apply> <ml:mult/> <ml:real>3.5</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="16220" left="30" top="572.25" width="246" height="12" align-x="30" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Distance From Centroid of Top Rebar To Bottom of Deck:</p> </text> </region> <region region-id="16221" left="342" top="573" width="48.75" height="16.5" align-x="360.75" align-y="582" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="tr">d</ml:id> <ml:apply> <ml:mult/> <ml:real>5.5</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="16222" left="30" top="596.25" width="262.5" height="12" align-x="30" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Distance From Centroid of Bottom Rebar To Bottom of Deck:</p> </text> </region> <region region-id="16223" left="342" top="597" width="51" height="16.5" align-x="363" align-y="606" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffffe1" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="br">d</ml:id> <ml:apply> <ml:mult/> <ml:real>1.5</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="14173" left="6" top="780.75" width="144" height="14.25" align-x="6" align-y="792" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <u> <inlineAttr line-through="false"> <c val="#00f">CALCULATION SECTION</c> </inlineAttr> </u> </b> </f> </p> </text> </region> <region region-id="12419" left="48" top="812.25" width="290.25" height="12" align-x="48" align-y="822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f">Calculate member forces at yield for subsequent calculations</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="12420" left="66" top="836.25" width="72" height="12" align-x="66" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Top Rebar Force</p> </text> </region> <region region-id="12478" left="198" top="837" width="57" height="16.5" align-x="216" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rt">P</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="yr">F</ml:id> <ml:id xml:space="preserve" subscript="rt">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="12479" left="294" top="837" width="50.25" height="16.5" align-x="310.5" align-y="846" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rt">P</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kip</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kip"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="14186" left="66" top="860.25" width="71.25" height="12" align-x="66" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Bot Rebar Force</p> </text> </region> <region region-id="14187" left="198" top="861" width="61.5" height="16.5" align-x="218.25" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rb">P</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="yr">F</ml:id> <ml:id xml:space="preserve" subscript="rb">A</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="14188" left="294" top="861" width="52.5" height="16.5" align-x="312.75" align-y="870" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rb">P</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kip</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kip"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="30"/> </region> <region region-id="12431" left="66" top="884.25" width="117" height="12" align-x="66" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Compression Flange Force</p> </text> </region> <region region-id="12484" left="198" top="885" width="63.75" height="16.5" align-x="214.5" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">P</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="yc">F</ml:id> <ml:id xml:space="preserve" subscript="c">b</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="c">t</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="12485" left="294" top="885" width="62.25" height="16.5" align-x="309" align-y="894" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">P</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kip</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2000</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kip"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="32"/> </region> <region region-id="12504" left="66" top="908.25" width="48" height="12" align-x="66" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Web Force</p> </text> </region> <region region-id="12505" left="198" top="909" width="66.75" height="16.5" align-x="216.75" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w">P</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="yw">F</ml:id> <ml:id xml:space="preserve">D</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">t</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="12506" left="294" top="909" width="64.5" height="16.5" align-x="311.25" align-y="918" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="w">P</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kip</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1400</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kip"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="34"/> </region> <region region-id="12513" left="66" top="932.25" width="93.75" height="12" align-x="66" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Tension Flange Force</p> </text> </region> <region region-id="12514" left="198" top="933" width="57.75" height="16.5" align-x="213" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t">P</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="yt">F</ml:id> <ml:id xml:space="preserve" subscript="t">b</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">t</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="12515" left="294" top="933" width="60.75" height="16.5" align-x="307.5" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t">P</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kip</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2000</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kip"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="12708" left="48" top="962.25" width="240.75" height="15" align-x="48" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f">Calculate M</c> </inlineAttr> </b> </f> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f"> <sub>p</sub> </c> </inlineAttr> </b> </f> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#00f"> and Y for all conditions (Table D6.1-2)</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="12710" left="66" top="986.25" width="135.75" height="12" align-x="66" align-y="996" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <u> <inlineAttr line-through="false"> <c val="#00f">Case I - Neutral axis in the web</c> </inlineAttr> </u> </f> </p> </text> </region> <region region-id="16247" left="552" top="1010.25" width="366.75" height="27" align-x="567.75" align-y="1020" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">03/04/2011 - Rewrote Case 1: Y<sub>1 </sub>equation from (Pt - Pc....) to (Pc - Pt....). Equation was written for positive flexure rather than negative.[Table D6.1-2]</p> </text> </region> <region region-id="12715" left="84" top="1006.5" width="147" height="35.25" align-x="101.25" align-y="1026" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">Y</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">D</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="c">P</ml:id> <ml:id xml:space="preserve" subscript="t">P</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="rt">P</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="rb">P</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">P</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="16243" left="336" top="1016.25" width="72" height="12" align-x="344.25" align-y="1026" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(from top of web)</p> </text> </region> <region region-id="15399" left="84" top="1047" width="105" height="16.5" align-x="102" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rt">d</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">Y</ml:id> <ml:id xml:space="preserve">Haunch</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="tr">d</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="15400" left="84" top="1071" width="109.5" height="16.5" align-x="104.25" align-y="1080" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="rb">d</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">Y</ml:id> <ml:id xml:space="preserve">Haunch</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="br">d</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="15401" left="84" top="1090.5" width="54.75" height="31.5" align-x="99" align-y="1110" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="t">d</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="1">Y</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="t">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="15402" left="84" top="1120.5" width="76.5" height="31.5" align-x="100.5" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">d</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">D</ml:id> <ml:id xml:space="preserve" subscript="1">Y</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">t</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="16241" left="822" top="1137" width="5.25" height="12.75" align-x="823.5" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:real xmlns:ml="http://schemas.mathsoft.com/math30">2</ml:real> </math> <rendering item-idref="42"/> </region> <region region-id="15403" left="432" top="1143" width="49.5" height="16.5" align-x="447.75" align-y="1152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" 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xml:space="preserve" subscript="t">P</ml:id> <ml:id xml:space="preserve" subscript="t">d</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="15405" left="432" top="1167" width="78.75" height="16.5" align-x="456" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p1">M</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">kip</ml:id> <ml:id xml:space="preserve">ft</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>12866.666666666666</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="foot"/> <unitReference unit="kip"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <decimal precision="0" show-trailing-zeros="true" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="45"/> </region> <region region-id="15406" left="66" top="1202.25" width="162.75" height="12" align-x="66" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <u> <inlineAttr font-style="normal" line-through="false"> <c val="#00f">Case II - Neutral axis in the top flange</c> </inlineAttr> </u> </f> </p> </text> </region> <region region-id="15407" left="84" top="1222.5" width="150" height="35.25" align-x="101.25" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">Y</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="t">t</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="w">P</ml:id> <ml:id xml:space="preserve" subscript="c">P</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="rt">P</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="rb">P</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="t">P</ml:id> </ml:apply> 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